Accounting for the variation in collision kerma-to-terma ratio in polyenergetic photon beam convolution

In photon beam convolution, the distribution of energy deposition about a primary photon interaction site due to charged particles set in motion at that site is represented by the primary kernel. Energy deposited due to scattered photons, bremsstrahlung, and annihilation photons is represented by the scatter kernel. As the energy deposited in each kernel voxel is normalized to the energy imparted at the interaction site, it is known as a fractional energy distribution. In terma-based convolution, where kernels are normalized to total energy imparted at the interaction site and are convolved with the terma in the dose calculation process, the sum of fractional energies contained in the primary kernel is equal to the ratio of collision kerma (Kc) to terma (T) corresponding to the energy spectrum used to generate the kernel. Since the ratio of collision kerma to terma increases with depth as the beam hardens, the integral fractional energy in a primary kernel formed for the spectrum at the surface is less than the ratio Kc/T at depth. This causes primary dose to be increasingly underestimated with depth and scatter dose to be increasingly overestimated. Single polyenergetic convolution (using polyenergetic primary and scatter kernels formed using a polyenergetic primary photon spectrum) is thus not as rigorous as if a separate convolution is performed for each energy component. The ratio of true primary dose to single polyenergetic primary dose increases almost linearly with depth and is almost equal to the Kc/T ratio. Primary and scatter dose are calculated correctly if a single polyenergetic convolution is performed in terms of Kc (for primary) and T-Kc (for scatter), where the kernels are weighted sums of monoenergetic kernels normalized to Kc and T-Kc. With this method, it is ensured that total primary energy deposited due to primary photon interactions in a unit mass at a point is equal to Kc at that point.